Determining approximate shortest paths on weighted polyhedral surfaces
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Bibliographic record
Abstract
In this article, we present an approximation algorithm for solving the single source shortest paths problem on weighted polyhedral surfaces. We consider a polyhedral surface P as consisting of n triangular faces, where each face has an associated positive weight. The cost of travel through a face is the Euclidean distance traveled, multiplied by the face's weight. For a given parameter ε, 0 <ε < 1, the cost of the computed paths is at most 1 + ε times the cost of corresponding shortest paths. Our algorithm is based on a novel way of discretizing polyhedral surfaces and utilizes a generic greedy approach for computing shortest paths in geometric graphs obtained by such discretization. Its running time is O(C(P) n /√ε log n /ε log 1/ε) time, where C(P) captures geometric parameters and the weights of the faces of P .
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.004 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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